A methodology is presented for the generation and meshing of large-scale three-dimensional random polycrystals. Voronoi tessellations are used and are shown to include morphological properties that ...make them particularly challenging to mesh with high element quality. Original approaches are presented to solve these problems: (i) “geometry regularization”, which consists in removing the geometrical details of the polycrystal morphology, (ii) “multimeshing” which consists in using simultaneously several meshing algorithms to optimize mesh quality, and (iii) remeshing, by which a new mesh is constructed over a deformed mesh and the state variables are transported, for large strain applications. Detailed statistical analyses are conducted on the polycrystal morphology and mesh quality. The results are mainly illustrated by the high-quality meshing of polycrystals with large number of grains (up to 10
5), and the finite element method simulation of a plane strain compression of
ε
=
1.4 of a 3000-grain polycrystal. The presented algorithms are implemented and distributed in a free (open-source) software package: Neper.
A full field crystal plasticity modelling of bimodal polycrystals is presented. Bimodal polycrystals are generated using a controlled Laguerre–Voronoi algorithm, and a modified phenomenological law ...is used to take into account the grain size effect through a Hall–Petch term. A focus is particularly made on the effects of grain size and of grain size ratio between ultrafine grains and coarse grains populations on local and global mechanical responses. The effect of the spatial distribution of the coarse grains (clustered or isolated) is also analysed in terms of strain localisation and stress concentration at the local scale.
A grain-based distinct element model featuring three-dimensional (3D) Voronoi tessellations (random poly-crystals) is proposed for simulation of crack damage development in brittle rocks. The grain ...boundaries in poly-crystal structure produced by Voronoi tessellations can represent flaws in intact rock and allow for numerical replication of crack damage progression through initiation and propagation of micro-fractures along grain boundaries. The Voronoi modelling scheme has been used widely in the past for brittle fracture simulation of rock materials. However the difficulty of generating 3D Voronoi models has limited its application to two-dimensional (2D) codes. The proposed approach is implemented in Neper, an open-source engine for generation of 3D Voronoi grains, to generate block geometry files that can be read directly into 3DEC. A series of Unconfined Compressive Strength (UCS) tests are simulated in 3DEC to verify the proposed methodology for 3D simulation of brittle fractures and to investigate the relationship between each micro-parameter and the model’s macro-response. The possibility of nu-merical replication of the classical U-shape strength curve for anisotropic rocks is also investigated in numerical UCS tests by using complex-shaped (elongated) grains that are cemented to one another along their adjoining sides. A micro-parameter calibration procedure is established for 3D Voronoi models for accurate replication of the mechanical behaviour of isotropic and anisotropic (containing a fabric) rocks.
► Hard X-ray nano-tomography has been used to investigate the microstructure of Ni–8YSZ substrate. ► A large reconstruction of 42
μm
×
42
μm
×
105
μm has been obtained. ► Such volume has been ...analysed to compute the morphological properties of the material. ► A tortuosity factor has been determined for this typical highly porous SOFC support.
A methodology, based on synchrotron X-ray nano-tomography measurements, is proposed to obtain 3D reconstructions of porous supports for Solid Oxide Fuel Cell (SOFC). The methodology has been applied to investigate the microstructure of a typical Ni–8YSZ cermet substrate of an Anode Supported Cell (ASC). Experimental conditions have been optimised so that a 3D reconstruction of 42
μm
×
42
μm
×
105
μm has been computed with a voxel size of 60
nm.
The 3D reconstruction has been numerically analysed showing a quasi isotropy over the medium. A special attention has been paid to compute the morphological properties controlling the gas diffusion through the support. In this frame, it has been found that a volume as large as 35
μm
×
35
μm
×
35
μm is required to be statistically representative for the whole substrate. More particularly, the tortuosity factor
τ has been calculated on the basis of finite element simulations. The effect of the boundary conditions taken for these simulations has been investigated. In the direction perpendicular to the anode/electrolyte interface, the tortuosity factor has been determined to
τ
z
=
2.8
−
0.2
+
0.3
.
Grain orientation fragmentation is studied in a set of 176 individual grains of an aluminium polycrystal deformed in plane strain compression at 400
°C to a strain of
ε
=
1.2
. Experimental ...observations were made by EBSD at successive strains of 0, 0.42, 0.77 and 1.2 on the internal surface of a split sample. Statistics of the in-grain orientation spreads were computed based on approximately 3000 orientation measurements per grain. A high-resolution finite element simulation (about 1000 elements per grain) was carried out on a polycrystal whose grains were assigned the initial experimental crystal orientations. The experimental and simulation results were compared in terms of the fractions of grains that exhibit fragmentation and the lattice orientations of the fragmenting grains. The numbers of fragmented grains increase with strain, reaching values of 10% in the experiment (2-D characterization) and 20% in the simulation (3-D characterization) at
ε
=
1.2
. For both experiment and simulation, fragmentation is more likely in grains whose lattice is symmetrically oriented with respect to the loading axes. Under plane strain compression, the orientations of the fragmented grains coincide with regions of orientation space in which the reorientation velocity field in the plane perpendicular to the reorientation velocity direction is unstable.
A FE modelling of the elastoplastic interactions occurring within a 3D polycrystal subjected to diffusive phase transformation is proposed. The parent polycrystal is represented by a Voronoi ...tessellation, where grains differ in shape, size and crystallographic orientation. Grains of the new phase nucleate at favourable sites of the parent polycrystal then grow isotropically, following specific kinetics. This process can result in various product polycrystal morphologies where grains are distinguished by their morphologies and their crystallographic orientations, and have crystalline properties different from those of the parent grains. Application is performed on the austenite-to-ferrite transformation of a low carbon steel, by analysing different basic cases of transformation history with different constitutive modellings. Microplasticity and its related internal stresses are shown to develop during the phase transformations and to affect significantly the elastoplasticity of the product medium.
Abstract
In this work, it is investigated how grain boundaries influence the local strain determination by the microstructural feature tracking (MFT) algorithm. In this method, tetrahedra are used as ...the strain calculation unit. We apply the MFT processing procedure on data obtained by a crystal plasticity finite element modeling (CPFEM) simulation to explore the uncertainties in the calculated strains caused by grain boundaries. Effects of tetrahedron types and radius ratios are discussed.
A split sample of Al–0.1%Mn has been deformed by a series of compression tests in a channel-die at 400
°C to a final strain of 1.6. The orientations of 176 grains in a
4
×
4
mm
2
internal surface ...were followed by high-resolution electron backscatter diffraction at four different strains to compare with crystal plasticity models. Typically 3000 orientations per grain were used to quantify the average lattice rotations of each grain together with their orientation spreads (termed microtexture tracking). The average orientations tend towards the standard
β
-fibre plane-strain compression texture components, albeit with some variations. The in-grain orientation spreads develop strongly at first, then tend to saturate at high strains. Finally, the influence of grain environment on lattice rotation is examined by means of the rotation “variability at constant orientation”. On average and at the beginning of the deformation, two grains of the same initial orientation, but different neighbours, would rotate by angles that vary by 25% and axes separated by 37°; their orientations at
ε
=
1.2
would vary by 12°.
The average rotations of 157 individual grains measured in an Al–0.1%Mn polycrystal deformed in hot plane-strain compression to a strain of 1.2 have been compared to the predictions from several ...crystal plasticity models. The Taylor model successfully predicts the distributions of the rotation angles, but overestimates the rate of evolution of the rotation axes, which explains the overestimation of the final texture. The model also provides a first-order agreement for the rotation axes and the final components of the individual grains. The discrepancies are related to the influence of grain interaction. The main mechanisms of texture development at the level of the individual grains are identified through an analysis of their orientation trajectories. The introduction of local grain interactions, which produce a rotation variability at constant orientation, is shown to weaken texture development.
The microstructure and microtexture evolution of the same 3 grains around a triple point has been followed during hot plane strain compression by electron backscattered diffraction (EBSD) up to a ...strain of 1.2. A large grained model alloy of Al–0.1
wt% Mn was deformed in the form of a split sample in channel die compression at 400
°C by 3 repeated cycles, each involving EBSD grain orientation mapping, hot deformation and quenching. Detailed substructure maps of 3 grains on an inner surface demonstrates that their dislocation substructure develops up to a strain of about 0.5 then stabilises at approximately constant size, disorientation distribution and boundary alignment. The results are consistent with the repolygonisation model of steady state sub-boundary creation and dissolution during hot deformation.
► Same area around triple point in Al followed by EBSD during hot deformation. ► Strains from 0 to 1.2 by intervals of about 0.4. ► Sub-grain microstructure and microtexture stabilise after strains of about 0.5. ► Results consistent with model of continuous creation and dissolution of sub-grains.
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